document.write( "Question 1197462: How many different professionals committees of 10 people can be formed, each containing at least 2 Professors, at least 3 Managers and 3 ICT Experts from list of 10 Professors, 6 Managers and 8 ICT Experts? \n" ); document.write( "

Algebra.Com's Answer #830747 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many different professionals committees of 10 people can be formed,
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document.write( "Below in the Table, all possible different numbers of participanting members\r\n" );
document.write( "are presented, satisfying the imposed conditions.\r\n" );
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document.write( "         T        A        B        L        E\r\n" );
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document.write( "    Professors     Managers    ICT experts   Total\r\n" );
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document.write( "       2              5             3         10\r\n" );
document.write( "       3              4             3         10\r\n" );
document.write( "       4              3             3         10\r\n" );
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document.write( "Now write the relevant formulas:\r\n" );
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document.write( "The number of different committees N(2P of 10, 5M from 6, 3E from 8) =  =  45 *  6 * 56 =  15120,\r\n" );
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document.write( "The number of different committees N(3P of 10, 4M from 6, 3E from 8) =  = 120 * 15 * 56 = 100800,\r\n" );
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document.write( "The number of different committees N(4P of 10, 3M from 6, 3E from 8) =  = 210 * 20 * 56 = 235200.\r\n" );
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document.write( "The total numbers of all possible committees is 15120 + 100800 + 235200 = 351120.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution is a simple and almost mechanical procedure.\r
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\n" ); document.write( "\n" ); document.write( "The problem teaches you to organize your data, your thoughts and your calculations systematically.\r
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